in my bio class we studied that when a protein is heated it changes its structure and becomes inactive. if that is the case, then y do we eat omellets when we the protein is no longer active? how is it helpful for us?

The protein just becomes non-functional...do you really need functioning egg proteins in you?
Digestion breaks everything down, our body uses the scrap to make new proteins...too bad we can't recycle at the protein level.

Living one day at a time; Enjoying one moment at a time; Accepting hardships as the pathway to peace; ~Niebuhr

The structure of the protein changes,not the aminoacids. Our body does not use proteins as they are. Proteins are broken down into aminoacids and then the body uses those aminoacids to sythesize its OWN proteins. ( In some cases proteins can also be used as energy source.)
Hope it is clear now.

It matters not how strait the gate
How charged with punishment the scroll
I am the Master of my fate
I am the Captain of my soul.

Think of it this way, everything you eat is iron, it doesn't matter what form it's in :nails, cars, giant robots etc... Your stomach melts all the metal and your cells use the metal to make new parts it needs. So it doesn't matter what form the protein comes in(what protein you eat), everything is broken down and used again. And of course proteins are necessary for building flesh so you do need a lot of protein in your diet.

Living one day at a time; Enjoying one moment at a time; Accepting hardships as the pathway to peace; ~Niebuhr

But you can also keep in mind that soft boiled eggs or still slightly liquid omelettes are so much better than their hard boil/dried out counter parts. But this has nothing to do with biology, it's just cooking. who will start a topic on salmonella in eggs?)

People say you shouldn't eat raw eggs because of salmonella.
But I know alot of people (my first grade teacher for one) who actually drink breakfast shakes with raw eggs in it. Plus I've heard of people actually cracking raw eggs and gulping down the yolks.

About that protein rich diet...
It does matter what kind of proteins you eat because you need to get all the essential aminoacids. For example: cereals contain a lot of proteins but are very poor in lisine and triptofan. Legumes are also rich in proteins but poor in metionine. So even if you have a protein-rich diet, if it made out completely of legumes it will not be healthy